Singularities of energy-minimizing vector-valued maps – SING

This project lies at the interface between Calculus of Variations, Partial Differential Equations and Nonlinear Analysis, with bridges to
Differential Geometry and Geometric Measure Theory. We pursue significant progress in the understanding of singularities which
arise in condensed matter physics, where equilibrium states are described by vector-valued maps minimizing a certain energy
functional. Our main motivations concern liquid crystals and micromagnetics, but the issues and methods are of broader
mathematical significance. We focus on three fundamental aspects: first, manifold-valued maps minimizing anisotropic energies, for
which crucial algebraic identities associated with isotropy are lost; second, smooth profiles describing the fine structure of
singularities, for which many existence, uniqueness, symmetry and stability issues are open; third, interparticle-like interactions of
singulatities predicted by renormalized energies.